Final answer:
By finding the constant of variation k using the given values of y=4 when x=2 and then substituting x=6 into the inverse variation formula, we find that y equals 4/3 or approximately 1.33 when x=6.
Step-by-step explanation:
If y varies inversely with x, it means that y can be expressed as y = k/x, where k is a constant.
To find the value of k, we use the given condition that y=4 when x=2.
We can set up an equation: 4 = k/2, which can be solved to find that k=8.
Now, to find y when x=6, we substitute k back into the inversely proportional equation:
y = 8/6.
Simplifying this gives us y = 4/3 or, in decimal form, approximately y = 1.33.